I'm not sure if this is the best place, but I need some mathematic insight! I'm working on signal deconvolution. These signals have an "almost" Gaussian shape, in the sense that the center up to 2 sigma is Gaussian (gaussian enough for what I need), but the left and right sides do not follow the same growth (left) or decay (right) curve. In particular, the right side can have a very long tail. I've been trying to find a set of equations that can fit the data peaks for several days now, but without success. Note that I don't need it to be perfect, just enough to fit reasonably well.
I've tried several methods, such as combining multiple Gaussians or using a sequence of Gaussians multiplied by an error function (someone's recommandation), but without success. The only thing that works reasonably well is using three Gaussians that I define over three different intervals, but it seems a bit clunky to me.
Here are two images, one in linear scale and one in log scale, of the type of data that I need to fit. On the log scale image, we can clearly see that there are three regimes. At around 16.00, we can see that the slope changes more or less abruptly.
I hope this could be still within the boundaries of "math stackexchange" as it is obviously not pure math.
Thank you in advance if you have any ideas/suggestions.
Having faced this kind of problems, I think that it would be of interest for you to look at what has been done in the area of spectroscopic data fitting (IR, UV, Raman, X-ray, ...).
The basic idea is to find the minimum number of base functions (Gaussian, Lorentzian, ...) to best fit a part of a spectrum.
You will find here, here, here some easily available ressources.